Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 2 cents, and 5 cents. Prove that a greedy algorithm always gives the optimal solution

Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 2 cents, and 5 cents. Prove that a greedy algorithm always gives the optimal solution

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Assume that you were given N cents (N is an integer) and you were asked to break up the N cents into coins consisting of 1 cent, 2 cents, and 5 cents.

Prove that a greedy algorithm always gives the optimal solution.

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The classic example of following a greedy algorithm is making change. Let’s say you buy some items at the store and the change from your purchase is 63 cents. How does the clerk determine the change to give you? If the clerkfollows a greedy algorithm, he or she gives you two quarters, a dime, and three pennies. That is the smallest number of coins that will equal 63 cents (given that we don’t allow fifty-cent pieces). It has been proven that an optimal solution for coin changing can always be found using the current American denominations of coins. However, if we introduce some other denomination to the mix, the greedy algorithm doesn’t produce an optimal solution.Write a program that uses a greedy algorithm to make change (this code assumes change of less than one dollar).